1. The IT Department at a large university wishes to estimate p = the proportion of students who own a computer with a 95% confidence interval. What is the minimum required sample size the IT Department should use to estimate the proportion p with a margin of error no larger than 3 percentage points?
A) 33 B) 752 C) 1067 D) 1068
Use the following to answer question 2.
The candy company that makes M&M's claims that 10% of the M&M's it produces are green. Suppose that the candies are packaged at in large bags of 200. When we randomly pick a bag of M&M's assume that this represents a simple random sample of size n = 200. Suppose we wish to test H0: p = 0.10 versus Ha: p 0.10.
2. If a 90% confidence interval were calculated from the same data, would it contain the value 0.10? A) Yes B) No
C) This cannot be determined from the information given.
Use the following to answer questions 3-4.
A psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if the card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime.
3. Based on the results of the test, what is a 95% confidence interval for p?
A) 0.25 ± 0.004 B) 0.25 ± 0.05 C) 0.25 ± 0.055 D) 0.25 ± 0.060
4. What do we know about the value of the P-value for the hypothesis test?
A) P-value < 0.001 B) 0.001 < P-value < 0.01
C) 0.01 < P-value < 0.05 D) 0.05 < P-value < 0.10
Use the following to answer question 5.
A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs. There were 3 types of helmets considered, classified according to liner type: suspension, padded-suspension, and padded. In the study, a measurement called the Gadd Severity Index (GSI) was obtained on each helmet using a standardized impact test. A helmet was deemed to have failed if the GSI was greater than 1200. Of the 81 helmets tested 29 failed the GSI 1200 criterion.
5. Based on the sample results, what is the 90% confidence interval estimate for the true population proportion of suspension helmets that would fail the test?
A) (0.304, 0.416) B) (0.256, 0.464) C) (0.213, 0.507) D) (0.272, 0.448)
6. A supplier of television through a satellite service is planning to offer a package and would like to determine what proportion of the households in their region would purchase this new package. Based on past experience it is thought that it is likely 25% to 35% of households will purchase the package. If the supplier wants to be 95% confident in the outcome, how many households should they randomly sample to achieve a margin of error no greater than ±0.025 in their estimate?
A) 922 B) 985 C) 350 D) 1399 E) Not within ± 25 of any of the above.
Use the following to answer question 7.
A study of newborns used umbilical cord blood to test for 25-hydroxy vitamin D, which is an indicator of vitamin D status of the baby. It was reported that 65% of babies tested were deficient in vitamin D. A researcher in a northern region felt that this percentage was too high for this region because with the reduced hours of sunshine during winter months pregnant women tended to use of higher doses of supplements to compensate. A sample of 125 newborns was tested, and 72 were declared to be deficient in vitamin D.
7. What would be the appropriate null and alternative hypotheses that the researcher should establish for a test of significance?
A) Ho: p = 0.5; Ha: p < 0.5B) Ho: p = 0.65; Ha: p 0.65
C) Ho: = 0.65; Ha: < 0.65 D) Ho: p = 0.65; Ha: p < 0.65
Use the following to answer question 8.
A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate. Using hospital birth records, she selects a sample of 200 couples that had children within the first 2 years of marriage. Following up on these couples, she finds that 80 couples are divorced within 5 years. Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.
8. Suppose the sociologist wishes to test H0: p = .5 versus Ha: p .5. At the 10% significance level, are the data statistically significant for testing these hypotheses?
A) Yes B) No
C) This cannot be determined from the information given.
Use the following to answer question 9.
A simple random sample of 60 households in the city of Greenville (call this city 1) is taken. In the sample, there are 45 households that decorate their houses with lights for the holidays. A simple random sample of 50 households is also taken from the neighboring town of Brownsboro (call this city 2). In the sample, there are 40 households that decorate their houses. We wish to estimate the difference in proportions of households that decorate their houses with lights for the holidays with a 95% confidence interval.
9. What is a 95% confidence interval for the difference in population proportions of households that decorate their houses with lights for the holidays?
A) (–0.181, 0.081) B) (–0.206, 0.106) C) (–0.231, 0.138) D) (–0.255, 0.155)
Use the following to answer question 10.
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands.
10. What is the 99% confidence interval estimate of the true difference, ?
A) (0.0042, 0.1584)
B) (0.0084, 0.1542)
C) (0.0005, 0.1621)
D) (–0.1893, 0.3897)
Answer Key - Untitled Exam-13
1. D
2. C
3. D
4. C
5. D
6. D
7. D
8. A
9. B
10. C